研一下四高高金课件lecture

1、Advanced Financial EconomicsLecture 12by Yinggang ZhouOutline (chapter 6)Gain from diversificationWhen correlation is 1, -1 and in between (-1,1)Minimum variance frontier (How to formulate it)? Efficient frontier (Upper portion of minimum variance frontier)Efficient frontier tangent to indifference

2、curve Optimal portfolio maximizing mean-variance preferenceCombine risky assets with risk-free assetAn additional and striking resultInvestors invest in the same two funds!No gain from perfect correlationRisk-return relation of portfolioGraphical illustrationWhat if correlation=-1?Risk-return relati

3、on of portfolioGraphical illustrationWhat if -1correlation1?we can compute the portfolio standard deviation and do it for various values of portfolio return to trace out risk-return relation, which has a sideways parabolic shapeRisk-return relation of portfolioExampleExample (continued)Example (cont

4、inued)Minimum variance frontier (MVF)How to formulate the idea?Three assets case Solve the optimization problemSolve a system of 3 linear equationsMore general formulationQuadratic programming problemMVF move with number of risky assetsEfficient frontier (EF)Mean-variance dominanceGraphical illustra

5、tion of mean-variance dominanceGraphical illustration of efficient frontierCombine efficient frontier with preferenceOptimal portfolio is tangent to efficient frontierAll investors choose optimal portfolios along the efficient frontierAn additional and striking resultWhat is risk-return relation?The risk-return relation is linear!Efficient frontier is linear too!Tangency portfolio and efficient frontierInvestors invest in the same two funds!Two fund (separation) theoremThe optimal portfolio of risky assets can be